id
stringlengths 12
18
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imagewidth (px) 645
3.8k
| options
stringlengths 17
1.44k
| answer
stringclasses 10
values | subject
stringclasses 1
value |
|---|---|---|---|---|
validation_Math_28 | ['Uncertain', 'Maybe', 'Unlikely', 'Probably not', 'No', 'Likely', 'Yes', 'Possibly'] | G | Math |
|
test_Math_11 | ['0.950', '0.985', '0.975', '0.970', '0.990', '0.980', '0.965', '0.960', '0.995'] | I | Math |
|
test_Math_170 | ['Z-test', 'One sample t-test', 'Chi-square test', 'None of the t-tests would be suitable', 'Dependent samples t-test', 'Analysis of Variance (ANOVA) test', 'Paired samples t-test', 'Independent samples t-test', 'Multiple samples t-test', 'Two sample t-test'] | D | Math |
|
test_Math_270 | ['2.7 feet per minute', '2.2 feet per minute', '2.1 feet per minute', '3.1 feet per minute', '2.4 feet per minute', '3.4 feet per minute', '2.9 feet per minute', '2.8 feet per minute', '3.2 feet per minute', '2.6 feet per minute'] | E | Math |
|
test_Math_290 | ['9.475', '7.256', '6.239', '4.828', '6.647', '10.568', '5.892', '7.991', '8.342'] | A | Math |
|
test_Math_80 | ['$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\cos({\\pi x})+1\\right)^{2}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,d x$', '$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin(\\frac{\\pi x}{2})+1\\right)^{2}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,d x$', '$V=2\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{2}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,dx$', '$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{2}-\\left(x^{4}+1\\right)^{2}\\,\\right]\\,d x$', '$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{2}-\\left(x^{2}+1\\right)^{2}\\,\\right]\\,d x$', '$V=2\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{3}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,d x$', '$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+2\\right)^{2}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,d x$', '$V=2\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{2}-\\left(x^{3}+2\\right)^{2}\\,\\right]\\,d x$', '$V=\\pi\\int_{\\,\\,0}^{\\,\\,1}\\left[\\left(\\sin({\\pi x})+1\\right)^{2}-\\left(x^{3}+1\\right)^{2}\\,\\right]\\,d x$'] | B | Math |
|
test_Math_492 | ['14', '8', '25', '7', '12', '10', '15', '11', '16', '9'] | J | Math |
|
test_Math_122 | ['$\\frac{BA}{EC}$', '$\\frac{EC}{CD}$', '$\\frac{CD}{BA}$', '$\\frac{EC}{BA}$', '$\\frac{BA}{EA}$', '$\\frac{EC}{EA}$', '$\\frac{CD}{EA}$', '$\\frac{EA}{EC}$', '$\\frac{EA}{CD}$', '$\\frac{EA}{BA}$'] | F | Math |
|
test_Math_247 | ['False', 'True'] | A | Math |
|
test_Math_164 | ['P4: x1 = 1.956, x2 = 5.998', 'P2: x1 = (5/2), x2 = 3', 'P1: x1 = (3/2), x2 = 3', 'P4: x1 = 2.5, x2 = 4.5', 'P1: x1 = 3, x2 = 3', 'P3: x1 = 1.956, x2 = 0.002', 'P2: x1 = 3, x2 = 4', 'P1: x1 = 2, x2 = 2', 'P2: x1 = 2, x2 = 4', 'P3: x1 = 1.5, x2 = 2.5'] | B | Math |
|
validation_Math_1 | ['0', '2', '3', 'Infinity', '-Infinity', 'Undefined', '-1', 'Not exist', '1'] | H | Math |
|
test_Math_201 | ['$\\angle ABC \\cong \\angle EFG$', '$\\angle CFB \\cong \\angle GEF$', '$\\angle DAB \\cong \\angle FGE$', '$\\angle ABF \\cong \\angle BFC$', '$\\angle EFB \\cong \\angle CFB$', '$\\angle CBF \\cong \\angle GFC$', '$\\angle CFG \\cong \\angle FCB$', '$\\angle BCF \\cong \\angle GFE$', '$\\angle FCB \\cong \\angle GEC$', '$\\angle BAF \\cong \\angle FCG$'] | G | Math |
|
validation_Math_16 | ['(2, 1)', '(1, 1)', '(1, 0)', '(3, 2)', '(2, 0)', '(2, 2)', '(3, 3)', '(3, 1)', '(0, 0)', '(0, 2)'] | A | Math |
|
test_Math_346 | ['TRUE', 'Only if it has an even number of vertices', 'FALSE', "Can't be determined without additional information", "Only if it's a complete graph", "Only if it's a tree", 'Depends on the number of edges', 'Depends on the number of vertices'] | A | Math |
|
test_Math_390 | ['$EKBCFGDH_A$', '$EHBCFGKD_A$', '$EDBKCFGH_A$', '$EBKCFGDH_A$', '$EKBCFGDH_D$', '$EDBCFGKH_B$', '$EHBCFGKD_B$', '$EKBCFGDH_B$', '$EDBCFGKH_C$', '$EDBCFGKH_A$'] | J | Math |
|
validation_Math_19 | ['{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_6$, $e_8$}', '{$e_2$, $e_4$, $e_8$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_5$, $e_7$, $e_8$}, {$e_6$, $e_8$}', '{$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_5$, $e_7$, $e_8$}, {$e_6$, $e_8$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_6$, $e_8$}, {$e_2$, $e_4$}', '{$e_1$, $e_8$}, {$e_2$, $e_3$, $e_8$}, {$e_3$, $e_7$}, {$e_5$, $e_7$, $e_8$}, {$e_6$, $e_8$}, {$e_2$, $e_3$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_5$, $e_8$}, {$e_6$, $e_8$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_6$, $e_8$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_3$, $e_7$}, {$e_5$, $e_7$, $e_8$}, {$e_6$, $e_8$}, {$e_2$, $e_4$}', '{$e_1$, $e_8$}, {$e_2$, $e_4$, $e_8$}, {$e_5$, $e_7$, $e_8$}, {$e_6$, $e_8$}'] | C | Math |
|
validation_Math_7 | ['(1), (3), (5), (6), (2), (4)', '(1), (5), (3), (4), (2), (6)', '(1), (3), (4), (5), (2), (6)', '(1), (2), (3), (4), (5), (6)', '(1), (4), (3), (2), (5), (6)', '(1), (3), (2), (4), (5), (6)', '(1), (4), (2), (3), (5), (6)', '(1), (3), (5), (2), (4), (6)', '(1), (2), (4), (3), (5), (6)', '(1), (2), (3), (5), (4), (6)'] | D | Math |
|
test_Math_279 | ['-2', '-1', '1', '0', '5', '2', "does not exist for h'(1)", 'not exist', '4', '3'] | F | Math |
|
test_Math_476 | ['2,5', '2,3', '1,2', '3,4', '4,3', '2,4', '2,2', '4,2', '3,3', '3,2'] | B | Math |
|
test_Math_115 | ['12', '22', '14', '10', '20', '16', '4', '8', '6', '18'] | I | Math |
|
validation_Math_5 | ['$\\int_{0}^{1.5}[g(x)-f(x)]\\,d x$', '$\\int_{0}^{1}[g(x)-f(x)]\\,d x$', '$\\int_{0}^{1.5}[f(x)-g(x)]\\,d x$', '$\\int_{1}^{2}[g(x)-f(x)]\\,d x$', '$\\int_{0}^{2}[g(x)-f(x)]\\,d x$', '$\\int_{0}^{2}[f(x)-g(x)]\\,d x$', '$\\int_{0}^{2}[f(x)+g(x)]\\,d x$', '$\\int_{0}^{1.5}[f(x)+g(x)]\\,d x$', '$\\int_{1}^{1.5}[f(x)-g(x)]\\,d x$', '$\\int_{0}^{1}[f(x)-g(x)]\\,d x$'] | C | Math |
|
validation_Math_14 | ['(a+b)/6+3', '(a+b-3)/6+3', '(a+b+6)/6', '(a-b+3)/6', '(-a-b)/6+3', '(-a-b+3)/6', '(-a+b+3)/6', '(a-b)/6+3', '(a+b+3)/6', '(-a+b)/6+3'] | J | Math |
|
test_Math_19 | ['2/3', '1/2', '3/2', '0', '3/4', '2', '1', '1/4', '5/4'] | B | Math |
|
validation_Math_4 | ['$y=\\sin 3\\pi x$', '$y=\\sin 2\\pi x$', '$y=\\cos 2\\pi x$', '$y=\\sec 2\\pi x$', '$y=\\tan 2\\pi x$', '$y=\\cot 2\\pi x$', '$y=\\cos \\pi x$', '$y=\\cos 3\\pi x$', '$y=\\csc 2\\pi x$', '$y=\\sin \\pi x$'] | C | Math |
|
test_Math_41 | ['60°', '40°', '20°', '55°', '35°', '25°', '30°', '50°', '15°', '45°'] | G | Math |
|
test_Math_257 | ['Omitting C is better', 'Both are equal', 'omitting A is better', 'Omitting both A and G is better', 'Omitting B is better', 'Neither provides a good lower bound', 'The answer depends on the specific values of the other nodes', 'omitting G is better'] | H | Math |
|
validation_Math_29 | ['2.7', '1.5', '2.5', '1.9', '2.0', '2.3', '1.7', '2.9', '2.1', '1.8'] | D | Math |
|
test_Math_12 | ['6.2 mm', '2.6 mm', '3.2 mm', '4.1 mm', '5 mm', '2.4 mm', '3.5 mm', '4.8 mm', '4.3 mm', '5.5 mm'] | I | Math |
|
validation_Math_22 | ['60', '209', '144', '157', '215', '162', '194', '115', '132', '178'] | G | Math |
|
test_Math_75 | ['A > B > C > D', 'C > D > A > B', 'B > C > A > D', 'A > C > B > D', 'B > C > D > A', 'B > A > C > D', 'C > B > A > D', 'D > C > B > A', 'D > A > B > C', 'B > D > A > C'] | F | Math |
|
validation_Math_17 | ['$\\theta = 4\\pi /3$', '$\\theta = \\pi /2$', '$\\theta = \\pi $', '$\\theta = \\pi /3$', '$\\theta = \\pi /4$', '$\\theta = 2\\pi $', '$\\theta = 5\\pi /6$', '$\\theta = 2\\pi /3$', '$\\theta = 3\\pi /2$', '$\\theta = 3\\pi /4$'] | B | Math |
|
test_Math_266 | ['112', '115', '113', '111', '114', '118', '110', '117', '116', '119'] | C | Math |
|
test_Math_224 | ['x = 0 and x = 1', 'x = 0', 'x = 3', 'x = 2', 'None of the above', 'x = -2', 'x = -1', 'x = -3', 'x = 1'] | A | Math |
|
validation_Math_20 | ['Graph G2 with vertices v1 to v8 and arcs including (v2, v5) and (v4, v8).', 'Graph G1 with vertices v1 to v8 and arcs including (v1, v3), (v2, v3) and so on.', 'Graph G2 with vertices v1 to v8 and no arc connecting A1 and A3.', 'Graph G1 with vertices v1 to v8 and arcs including (v2, v5), (v4, v8), and (v1, v6).', 'Graph G1 with vertices v1 to v8 and arcs excluding (v2, v5) and (v4, v8).', 'Graph G2 with vertices v1 to v8 and arcs including (v3, v7) and (v2, v6).', 'Graph G1 with vertices v1 to v8 and no arc connecting A2 and A4.', 'Graph G2 with vertices v1 to v8 and arcs excluding (v4, v8) and (v1, v3).', 'Graph G1 with vertices v1 to v8 and arcs including (v1, v3) and (v2, v5).', 'Graph G2 with vertices v1 to v8 and arcs excluding (v1, v3) and (v2, v5).'] | A | Math |
|
test_Math_435 | ['Introduce a very large amount in one of the zero boxes and calculate the total shipping cost.', 'Introduce a very small amount in one of the zero boxes and calculate the total shipping cost.', 'Consider only the indirect routes for shipment, ignoring the direct routes.', 'Assign a value of zero to the box with the smallest cost.', 'Increase the cost of the most expensive route to make other routes more viable.', "Assign a value of zero to the box with the d entry in the final solution if it's still present.", 'Consider only the direct routes for shipment, ignoring the indirect routes.', 'Remove the highest cost box to simplify the solution.', 'Assign a value of one to the box with the highest cost.', 'Remove all the zero boxes to simplify the solution.'] | F | Math |
|
validation_Math_25 | ['$\\theta $ = 1.221', '$\\theta $ = 0.785', '$\\theta $ = 1.047', '$\\theta $ = 1.475', '$\\theta $ = 0.853', '$\\theta $ = 1.178', '$\\theta $ = 1.396', '$\\theta $ = 1.570', '$\\theta $ = 0.524', '$\\theta $ = 1.309'] | D | Math |
|
test_Math_475 | ['0.58m/min', '0.64m/min', '0.69m/min', '0.70m/min', '0.61m/min', '0.60m/min', '0.52m/min', '0.72m/min', '0.67m/min', '0.55m/min'] | B | Math |
|
validation_Math_30 | ['$\\sqrt{2} - 1$', '$\\frac{\\sqrt{2}}{3}$', '$1-\\frac{\\sqrt{2}}{4}$', '$\\frac{1}{2}$', '$\\frac{2}{3}$', '$1-\\sqrt{2}$', '$\\frac{1}{3}$', '$2-\\sqrt{2}$', '$1-\\frac{1}{\\sqrt{2}}$', '$\\frac{3}{4}$'] | H | Math |
|
test_Math_282 | ['300', '720', '600', '1080', '540', '450', '900', '360', '270', '120'] | E | Math |
|
test_Math_18 | ['Yes', 'Insufficient information', 'Multiple answers possible', 'All tickets not used', 'Incorrect order', 'Partially correct', 'No', 'Some tickets used more than once'] | A | Math |
|
test_Math_56 | ['$450,000', '$500,000', '$200,000', '$550,000', '$350,000', '$250,000', '$600,000', '$300,000', '$150,000', '$400,000'] | A | Math |
|
test_Math_65 | ['15.2%', '17.6%', '19.2%', '20.1%', '14.3%', '13.7%', '12.9%', '12.5%', '16.4%', '18.5%'] | E | Math |
|
test_Math_393 | ['$\\overline{A E} \\cong \\overline{B E}$', '$\\overline{A D} \\parallel \\overline{B C}$', '$\\triangle A E C \\sim \\triangle B E D$', '$\\angle A C B \\cong \\angle C B D$', '$\\angle A E C \\cong \\angle B E D$', '$\\overparen{C B} \\cong \\overparen{D A}$', '$\\triangle A E C \\cong \\triangle B E D$', '$\\angle A D E \\cong \\angle B C E$', '$\\triangle C A E \\cong \\triangle D B E$', '$\\overparen{C A} \\cong \\overparen{D B}$'] | C | Math |
|
validation_Math_8 | ['4 boats of Type 1 and 2 boats of Type 2', '4 boats of Type 1 and 1 boat of Type 2', '7 boats of Type 1 and 0 boats of Type 2', '1 boat of Type 1 and 3 boats of Type 2', '2 boats of Type 1 and 3 boats of Type 2', '5 boats of Type 1 and 0 boats of Type 2', '3 boats of Type 1 and 2 boats of Type 2', '6 boats of Type 1 and 0 boats of Type 2', '3 boats of Type 1 and 1 boat of Type 2', '2 boats of Type 1 and 2 boats of Type 2'] | F | Math |
|
test_Math_504 | ['Earliest times: A-1, B-4, C-7, D-14, E-18, F-21, G-24, H-27; Latest times: A-1, B-5, C-8, D-16, E-20, F-24, G-28, H-31; Critical path: ACEGH', 'Earliest times: A-0, B-4, C-9, D-15, E-20, F-24, G-27, H-31; Latest times: A-0, B-5, C-10, D-16, E-22, F-25, G-28, H-32; Critical path: ABDEH', 'Earliest times: A-0, B-6, C-9, D-17, E-22, F-24, G-27, H-28; Latest times: A-0, B-8, C-9, D-17, E-23, F-25, G-27, H-28; Critical path: ACDGH', 'Earliest times: A-1, B-5, C-8, D-14, E-18, F-21, G-25, H-29; Latest times: A-1, B-6, C-9, D-15, E-20, F-24, G-28, H-32; Critical path: ACEFH', 'Earliest times: A-0, B-5, C-10, D-15, E-20, F-23, G-26, H-30; Latest times: A-0, B-5, C-10, D-15, E-21, F-23, G-26, H-30; Critical path: ABFGH', 'Earliest times: A-0, B-3, C-8, D-16, E-19, F-23, G-26, H-29; Latest times: A-0, B-4, C-8, D-17, E-20, F-24, G-27, H-30; Critical path: BCEFH', 'Earliest times: A-0, B-5, C-8, D-13, E-18, F-21, G-25, H-29; Latest times: A-0, B-6, C-9, D-14, E-20, F-24, G-28, H-33; Critical path: ABDEH', 'Earliest times: A-0, B-3, C-7, D-13, E-19, F-22, G-25, H-28; Latest times: A-0, B-5, C-8, D-15, E-21, F-26, G-30, H-33; Critical path: ABDGH', 'Earliest times: A-2, B-6, C-9, D-12, E-18, F-21, G-24, H-27; Latest times: A-2, B-7, C-9, D-13, E-18, F-22, G-24, H-27; Critical path: ADEGH', 'Earliest times: A-0, B-7, C-8, D-15, E-19, F-21, G-25, H-27; Latest times: A-0, B-7, C-9, D-17, E-23, F-26, G-29, H-32; Critical path: ABDFH'] | C | Math |
|
test_Math_341 | ['O-B, B-A, A-C, B-E, E-D, D-T', 'O-B, A-B, A-C, C-E, E-D, D-T', 'O-A, A-B, B-C, B-E, E-D, D-T', 'O-A, A-C, B-C, B-E, E-D, D-T', 'O-A, A-B, C-B, C-E, E-D, D-T', 'O-B, B-A, A-C, C-E, E-D, D-T', 'O-A, A-B, B-C, C-E, E-D, D-T', 'O-A, A-B, B-C, C-E, E-D, T-D', 'O-A, A-B, B-E, E-D, D-T, T-C', 'O-A, A-B, B-C, B-E, E-D, D-C'] | C | Math |
|
validation_Math_2 | ['(a) 3, (b) 3', '(a) 4, (b) 2', '(a) 3, (b) 1', '(a) 1,(b) 3', '(a) 1,(b) 2', '(a) 3, (b) 2', '(a) 2, (b) 3', '(a) 1, (b) 4', '(a) 2,(b) 2', '(a) 2, (b) 4'] | G | Math |
|
test_Math_189 | ['$35 million', '$50 million', '$45 million', '$55 million', '$10 million', '$25 million', '$40 million', '$30 million', '$20 million', '$15 million'] | A | Math |
|
test_Math_222 | ['$\\int_{3.250}^{5.340}h(t)\\,d t$', '$\\int_{3.500}^{5.450}h(t)\\,d t$', '$\\int_0^{3.694}h^{\\prime}(t)\\,d t$', '$\\int_{3.666}^{5.390}h(t)\\,d t$', '$\\int_{1.400}^{4.755}h^{\\prime}(t)\\,d t$', '$\\int_{2.890}^{5.450}h(t)\\,d t$', '$\\int_{1.355}^{4.650}h^{\\prime}(t)\\,d t$', '$\\int_{2.345}^{3.890}h^{\\prime}(t)\\,d t$', '$\\int_{1.855}^{4.900}h^{\\prime}(t)\\,d t$', '$\\int_{1.355}^{4.650}h(t)\\,d t$'] | D | Math |
|
test_Math_16 | ['$7\\pi$', '$6\\pi$', '$5\\pi$', '$9\\pi$', '$2\\pi$', '$16\\pi$', '$4\\pi$', '$3\\pi$', '$\\pi$', '$8\\pi$'] | E | Math |
|
validation_Math_27 | ['12', '13', '6.7', '2.4', '8', '15', '11', '7', '10', '9'] | F | Math |
|
validation_Math_3 | ['<image 2>', '<image 1>', '<image 3>'] | A | Math |
|
test_Math_165 | ['$6\\frac{3}{4}$', '$7\\frac{1}{4}$', '$8\\frac{3}{5}$', '$7\\frac{1}{2}$', '$5\\frac{1}{4}$', '$8$', '$4\\frac{3}{5}$', '$6\\frac{1}{2}$', '5', '$9\\frac{1}{2}$'] | H | Math |
|
validation_Math_12 | ['d_1^* = 0 and d_2^* = S_2 or S_3 and d_3^* = 0', 'd_1^* = 0 and d_2^* = S_2 and d_3^* = 0', 'd_1^* = S_1 or 0 and d_2^* = 0 and d_3^* = 0', 'd_1^* = S_1 and d_2^* = 0 and d_3^* = S_3', 'd_1^* = S_1 and d_2^* = S_2 and d_3^* = S_3', 'd_1^* = S_1 and d_2^* = S_2 and d_3^* = 0', 'd_1^* = 0 and d_2^* = S_2 and d_3^* = S_3', 'd_1^* = S_1 and d_2^* = S_2 and d_3^* = S_3 or 0', 'd_1^* = 0 and d_2^* = 0 and d_3^* = S_3', 'd_1^* = S_1 and d_2^* = 0 and d_3^* = 0 or S_3'] | J | Math |
|
test_Math_205 | ['$A G=B G$', '$\\angle B G C \\cong \\angle B G A$', '$A G=C G$', '$\\angle A E B \\cong \\angle A E C$', '$D G=E G$', '$\\angle A B G \\cong \\angle A E C$', '$\\angle D A B \\cong \\angle E A B$', '$\\angle A G B \\cong \\angle A G C$', '$\\angle D B G \\cong \\angle E B G$', '$B G=D G$'] | I | Math |
|
test_Math_22 | ['2/3', '3', '1/3', '0', '4', '3/2', '1/4', '1', '2', '1/2'] | H | Math |
|
test_Math_436 | ['5:4', '8:3', '2:1', '6:5', '5:3', '5:2', '4:3', '7:3', '3:2', '1:1'] | C | Math |
|
validation_Math_24 | ['r = R/3', 'r = 3R/2', 'r = 5R/3', 'r = R/4', 'r = 2R/3', 'r = R/5', 'r = 3R', 'r = 4R/3', 'r = R/2', 'r = 2R'] | E | Math |
|
test_Math_209 | ['65ft', '100ft', '75ft', '37.5ft', '80ft', '35.5ft', '45ft', '50ft', '150ft', '60ft'] | C | Math |
|
validation_Math_26 | ['$\\int_{0}^{a}\\left[b-f(x)-g(x)\\right]d x$', '$\\int_{0}^{a}\\left[g(x)-b+f(x)\\right]d x$', '$\\int_{0}^{a}\\left[f(x)-g(x)\\right]d x$', '$\\int_{0}^{a}\\left[b-g(x)+f(x)\\right]d x$', '$\\int_{0}^{a}\\left[f(x)-b+g(x)\\right]d x$', '$\\int_{0}^{a}\\left[b+g(x)-f(x)\\right]d x$', '$\\int_{0}^{a}\\left[g(x)+f(x)\\right]d x$', '$\\int_{0}^{a}\\left[b-g(x)-f(x)\\right]d x$', '$\\int_{0}^{a}\\left[b+g(x)+f(x)\\right]d x$', '$\\int_{0}^{a}\\left[g(x)-f(x)\\right]d x$'] | D | Math |
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